Prove `1.4.7+2.5.8+3.6.9+.......` upto n terms `=(n)/(4)(n+1)(n+6)(n+7)`

By using the Principle of Mathematical Induction, prove the following for all n in N : 1.4.7+2.5.8+3.6.9+.......+ n(n + 3)(n+ 6)= n/4 (n +1)(n+ 6)(n+ 7) .

2.5+3.8+4.11+.....+ upto n terms =n(n^(2)+4n+5), n in N

3.6+4.7+5.8+.....+(n-2) terms =

2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

By method of induction, prove that 1.6 + 2.9 + 3.12 +... +to n terms = n(n +1 )(n+2) for all n in N .

Find 1.4.7 + 3.6.9 + 5.8.11 + 7.10.13 …. Upto 'n' term.

Prove the following by the method of induction for all n in N : 1.3 + 3.5 + 5.7 +... to n terms =n/3 (4n^2 + 6n - 1) .

Using the principle of finite Mathematical Indcution prove that 2.3 + 3.4 + 4.5 + ……."upto n terms" = (n(n^(2)+6n+11))/(3) .